A novel framework for fluid/structure interaction in subject-specific surgical simulations involving elastic cardiac geometries

涉及弹性心脏几何形状的特定主题手术模拟中流体/结构相互作用的新框架

• 批准号: 0914813
• 负责人: Joseph Teran
• 金额: $ 19.71万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0914813&HistoricalAwards=false
• 关键词: novel; framework; fluid; structure; interaction

One of the most important applications of computational fluid dynamics has been simulation of blood flow. However, practical difficulties have limited the types and applicability of simulations performed, thus preventing numerical modeling of blood flow from reaching its full potential. Extreme computational expense, reduced order of accuracy due to complex geometry and lack of regularity in solutions have restricted the scale and scope of blood flow simulations. One exciting application currently outside the scope of existing methods is the simulation of surgeries designed to repair diseased and malfunctioning heart valves. The complexity of the valvular geometry and flow patterns in their vicinity complicate considerably the development of reliable and predicative numerical models. The ability to deliver patient specific prognoses demands an algorithm that can accurately resolve these flows. However, cardiac geometry is highly complicated and must be represented with both volumetric and membraneous components, either of which might also exhibit intricate irregularities due to the patient's valvular disease. The solid/fluid coupling algorithm must have sufficient geometric flexibility to resolve these features and to adapt to the changes induced by the virtual surgery. Ultimately, to provide meaningful results the solid/fluid algorithm must deliver a certain level of accuracy and stability without sacrificing adaptability. Existing methods for fluid-solid interaction cannot guarantee this level of functionality. The general case sees geometric flexibility traded for higher order accuracy. Also, practical demands create the need for stable algorithms with minimal time step restrictions as the desire to accurately predict postoperative behavior comes with the inherent need to run simulations over longer time intervals. The challenging nature of providing the functionality needed for effectively simulating valvular surgeries requires addressing all these issues simultaneously and existing methods cannot do this. The primary contribution of the proposed research will be the development and application of a tractable second-order numerical method capable of coupling a viscous incompressible fluid with thin and volumetric geometrically complex elastic solids represented with Lagrangian meshes. The fluid will be modeled by a cartesian Eulerian grid in which the solid representations are embedded to avoid the prohibitive cost of re-meshing the computational domain at each time-step in the simulation. Regular grids will be used wherever possible. Geometric flexibility and the ability to impose a variety of boundary conditions on arbitrary moving surfaces throughout the fluid domain are key to accomplishing the stated goals and will be a primary guide in developing the higher-order accurate Navier-Stokes solver.The benefits of patient-specific computational fluid dynamics simulations of blood flow near healthy and diseased heart valves can potentially revolutionize the treatment of certain pathologies. Such functionality could allow the surgeon to design new procedures tailored to the individual, to determine whether or not surgery is needed by numerically predicting postoperative results and could even be used to train surgical residents in state-of-the-art techniques. This effort will focus on the development of a numerical method for examining blood flow through such surgically altered tissues in the challenging case of corrective valvular surgery. Specifically, we target improvements in treatment for Tetralogy of Fallot and mitral valve repair. Patients born with Tetralogy of Fallot require artificial replacement valves with inherently finite lifespan and accurate determination of the time to replace these valves to correct for pulmonary regurgitation is a matter of life and death. With procedures such as mitral valve repair, the difficult choice lies in determining exactly which type of correction best suits a particular individual. The determination of when to make these critical decisions and many related others could potentially be improved with the successful application of this effort.

计算流体动力学最重要的应用之一是模拟血液流动。然而，实际困难限制了模拟的类型和适用性，从而阻止了血流的数值模拟发挥其全部潜力。极端的计算费用，由于复杂的几何形状和缺乏规律性的解决方案，降低了精度的顺序限制了血流模拟的规模和范围。目前在现有方法范围之外的一个令人兴奋的应用是模拟旨在修复患病和故障心脏瓣膜的手术。瓣膜的几何形状及其附近的流动模式的复杂性，大大复杂的可靠和预测的数值模型的发展。提供患者特定流量的能力需要一种能够准确解析这些流量的算法。然而，心脏的几何形状是非常复杂的，必须表示与体积和膜组件，其中任何一个也可能表现出复杂的不规则性，由于病人的瓣膜疾病。固体/流体耦合算法必须具有足够的几何灵活性，以解决这些功能，并适应虚拟手术引起的变化。最终，为了提供有意义的结果，固体/流体算法必须在不牺牲适应性的情况下提供一定水平的准确性和稳定性。现有的流体-固体相互作用方法不能保证这种水平的功能。一般情况下，几何灵活性换取更高的精度。此外，实际需求产生了对具有最小时间步长限制的稳定算法的需求，因为准确预测术后行为的愿望伴随着在更长时间间隔上运行模拟的固有需求。提供有效模拟瓣膜手术所需的功能的挑战性本质要求同时解决所有这些问题，而现有方法无法做到这一点。拟议的研究的主要贡献将是一个易于处理的二阶数值方法的开发和应用，能够耦合粘性不可压缩流体与薄和体积几何复杂的弹性固体与拉格朗日网格表示。流体将通过嵌入固体表示的笛卡尔欧拉网格进行建模，以避免在模拟中的每个时间步重新网格化计算域的高昂成本。将尽可能使用规则网格。几何灵活性和在整个流体域的任意移动表面上施加各种边界条件的能力是实现所述目标的关键，并且将是开发高阶精确Navier-Stokes solver.The患者特定的健康和患病心脏瓣膜附近血流的计算流体动力学模拟的益处可能会彻底改变某些病理的治疗。这种功能可以允许外科医生设计适合个人的新程序，通过数值预测术后结果来确定是否需要手术，甚至可以用于培训外科住院医生的最先进技术。这项工作将集中在发展一种数值方法，用于检查在具有挑战性的情况下，矫正瓣膜手术，通过这种手术改变组织的血流。具体来说，我们的目标是改善法洛四联症和二尖瓣修复术的治疗。出生时患有法洛四联症的患者需要具有固有有限寿命的人工置换瓣膜，并且准确确定置换这些瓣膜以纠正肺动脉返流的时间是生死攸关的问题。对于二尖瓣修复等手术，困难的选择在于确定哪种类型的矫正最适合特定的个体。如果成功地应用这一努力，就有可能改进何时作出这些关键决定和许多其他相关决定的决定。